Question: If $a + b + c = 1$ and $x + y + z = 1$, what is $5b + 5c - 2y - 2z + 5a - 2x$ ?
$= 5a + 5b + 5c - 2x - 2y - 2z$ $= (5) \cdot (a + b + c) + (-2) \cdot (x + y + z)$ $= (5) \cdot (1) + (-2) \cdot (1)$ $= 5 - 2$ $= 3$